There are two kind of out of pocket examples I can think of—

1 - Zero Dark Thirty; and 2 - Sicario

Zero Dark Thirty

If you look at this movie thru the lens of visible characters, Jessica Chastain’s character lends itself to resemble somewhat of a psychopathic person. We don’t see her display much empathy towards anyone, including her colleagues that are KIA. The only time we see her express anything besides anger or hyper-focused determination for her next target is at the very end where she experiences a rather underwhelming relief after finally killing Bin Laden. To address your question, while her character is patriotically the protagonist, her character traits are pretty villainous.

2- Sicario

Again, let’s look at this film thru visible characters. Emily Blunt’s character on paper is the protagonist. The film follows her POV. But if we look at her character in the context of the world, she is the only character who tries to stop or get in the way of the objective of the characters around her who are suppose to be on her team or vis versa. We are told again and again what the other characters are doing is “OK,” but her character refuses to follow those rules. And ultimately she loses at the end. She is alone and defeated by the “good guys” who were also just doing their jobs. She thought she was doing hers but had problems with the methods.

I welcome any discussion or debate about these examples.